Speaking only of Touhou, from what I've seen characters keep their hat a lot more often than not even when nude, and to the point it's kind of common knowledge (you know, hats = people jokes and all). Reasonable expectations become hats everywhere regardless of the situation.
But, it's true that given this context, characters who have lost their hat are most likely not in their normal outfit.

... Honestly, the more I think about it, the more complicated it gets. I think I'll give my vote to costumes just because it means less work.

It will probably need some additional rules over time though, because of cases like Kirisame_Marisa kiss where artists purposedly cut the hat off of her outfit so it doesn't get in the way.